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Author: Christopher Pincock
Publisher: Oxford University Press
ISBN: 0190208570
Category : Philosophy
Languages : en
Pages : 352
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Book Description
Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics.
Author: Christopher Pincock
Publisher: Oxford University Press
ISBN: 0190208570
Category : Philosophy
Languages : en
Pages : 352
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Book Description
Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics.
Author: Christopher Pincock
Publisher: OUP USA
ISBN: 0199757100
Category : Mathematics
Languages : en
Pages : 347
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Book Description
Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. Pincock tackles this perennial question by asking how mathematics contributes to the success of our best scientific representations.
Author: Roman Frigg
Publisher: Springer
ISBN: 9783030451554
Category : Philosophy
Languages : en
Pages : 241
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Book Description
This monograph offers a critical introduction to current theories of how scientific models represent their target systems. Representation is important because it allows scientists to study a model to discover features of reality. The authors provide a map of the conceptual landscape surrounding the issue of scientific representation, arguing that it consists of multiple intertwined problems. They provide an encyclopaedic overview of existing attempts to answer these questions, and they assess their strengths and weaknesses. The book also presents a comprehensive statement of their alternative proposal, the DEKI account of representation, which they have developed over the last few years. They show how the account works in the case of material as well as non-material models; how it accommodates the use of mathematics in scientific modelling; and how it sheds light on the relation between representation in science and art. The issue of representation has generated a sizeable literature, which has been growing fast in particular over the last decade. This makes it hard for novices to get a handle on the topic because so far there is no book-length introduction that would guide them through the discussion. Likewise, researchers may require a comprehensive review that they can refer to for critical evaluations. This book meets the needs of both groups.
Author: Emily R. Grosholz
Publisher:
ISBN: 9781280809743
Category :
Languages : en
Pages : 172
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Book Description
Author: James Nguyen
Publisher: Cambridge University Press
ISBN: 1009007343
Category : Science
Languages : en
Pages : 154
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Book Description
This Element presents a philosophical exploration of the notion of scientific representation. It does so by focussing on an important class of scientific representations, namely scientific models. Models are important in the scientific process because scientists can study a model to discover features of reality. But what does it mean for something to represent something else? This is the question discussed in this Element. The authors begin by disentangling different aspects of the problem of representation and then discuss the dominant accounts in the philosophical literature: the resemblance view and inferentialism. They find them both wanting and submit that their own preferred option, the so-called DEKI account, not only eschews the problems that beset these conceptions, but further provides a comprehensive answer to the question of how scientific representation works. This title is also available as Open Access on Cambridge Core.
Author: John K. Gilbert
Publisher: Springer Science & Business Media
ISBN: 1402052677
Category : Education
Languages : en
Pages : 326
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Book Description
External representations (pictures, diagrams, graphs, concrete models) have always been valuable tools for the science teacher. This book brings together the insights of practicing scientists, science education researchers, computer specialists, and cognitive scientists, to produce a coherent overview. It links presentations about cognitive theory, its implications for science curriculum design, and for learning and teaching in classrooms and laboratories.
Author: Catelijne Coopmans
Publisher: MIT Press
ISBN: 0262525380
Category : Social Science
Languages : en
Pages : 381
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Book Description
A fresh approach to visualization practices in the sciences that considers novel forms of imaging technology and draws on recent theoretical perspectives on representation. Representation in Scientific Practice, published by the MIT Press in 1990, helped coalesce a long-standing interest in scientific visualization among historians, philosophers, and sociologists of science and remains a touchstone for current investigations in science and technology studies. This volume revisits the topic, taking into account both the changing conceptual landscape of STS and the emergence of new imaging technologies in scientific practice. It offers cutting-edge research on a broad array of fields that study information as well as short reflections on the evolution of the field by leading scholars, including some of the contributors to the 1990 volume. The essays consider the ways in which viewing experiences are crafted in the digital era; the embodied nature of work with digital technologies; the constitutive role of materials and technologies—from chalkboards to brain scans—in the production of new scientific knowledge; the metaphors and images mobilized by communities of practice; and the status and significance of scientific imagery in professional and popular culture. Contributors Morana Alač, Michael Barany, Anne Beaulieu, Annamaria Carusi, Catelijne Coopmans, Lorraine Daston, Sarah de Rijcke, Joseph Dumit, Emma Frow, Yann Giraud, Aud Sissel Hoel, Martin Kemp, Bruno Latour, John Law, Michael Lynch, Donald MacKenzie, Cyrus Mody, Natasha Myers, Rachel Prentice, Arie Rip, Martin Ruivenkamp, Lucy Suchman, Janet Vertesi, Steve Woolgar
Author: Avi Wigderson
Publisher: Princeton University Press
ISBN: 0691189137
Category : Computers
Languages : en
Pages : 434
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Book Description
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author: Berinderjeet Kaur
Publisher: World Scientific
ISBN: 9813224231
Category : Mathematics
Languages : en
Pages : 395
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Book Description
This book contributes towards the literature in the field of mathematics education, specifically on aspects of empowering learners of mathematics. The book, comprising eighteen chapters, written by renowned researchers in mathematics education, provides readers with approaches and applicable classroom strategies to empower learners of mathematics.The chapters in the book can be classified into four sections. The four sections focus on how learners could be empowered in their learning, cognitive and affective processes, through mathematical content, purposefully designed mathematical tasks, whilst developing 21st century competencies.
Author: Anton Alekseev
Publisher: Birkhäuser
ISBN: 9783030781477
Category : Mathematics
Languages : en
Pages : 643
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Book Description
Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.
